

'''simple docstring'''





from __future__ import annotations

import time
from collections.abc import Sequence
from random import randint

from matplotlib import pyplot as plt






def 				_lowerCAmelCase			(   __magic_name__						:     Sequence[float]   , __magic_name__						:     int   , __magic_name__						:     int						)				->  tuple[int | None, int | None, float]:
						if not arr:
												return None, None, 0
						if low == high:
												return low, high, arr[low]

						lowercase :							Optional[int]    		=(low + high) // 2
						lowercase		,	lowercase		,	lowercase :							Optional[Any]    		=max_subarray(__magic_name__   , __magic_name__   , __magic_name__						)
						lowercase		,	lowercase		,	lowercase :							Union[str, Any]    		=max_subarray(__magic_name__   , mid + 1   , __magic_name__						)
						lowercase		,	lowercase		,	lowercase :							Any    		=max_cross_sum(__magic_name__   , __magic_name__   , __magic_name__   , __magic_name__						)
						if left_sum >= right_sum and left_sum >= cross_sum:
												return left_low, left_high, left_sum
						elif right_sum >= left_sum and right_sum >= cross_sum:
												return right_low, right_high, right_sum
						return cross_left, cross_right, cross_sum






def 				_lowerCAmelCase			(   __magic_name__						:     Sequence[float]   , __magic_name__						:     int   , __magic_name__						:     int   , __magic_name__						:     int						)				->  tuple[int, int, float]:
						lowercase		,	lowercase :							str    		=float('''-inf'''						), -1
						lowercase		,	lowercase :							List[Any]    		=float('''-inf'''						), -1

						lowercase :							int | float    		=0
						for i in range(__magic_name__   , low - 1   , -1						):
												summ += arr[i]
												if summ > left_sum:
																		lowercase :							List[Any]    		=summ
																		lowercase :							Tuple    		=i

						lowercase :							str    		=0
						for i in range(mid + 1   , high + 1						):
												summ += arr[i]
												if summ > right_sum:
																		lowercase :							Optional[Any]    		=summ
																		lowercase :							Union[str, Any]    		=i

						return max_left, max_right, (left_sum + right_sum)






def 				_lowerCAmelCase			(   __magic_name__						:     int						)				->  float:
						lowercase :							str    		=[randint(1   , __magic_name__						) for _ in range(__magic_name__						)]
						lowercase :							Tuple    		=time.time()
						max_subarray(__magic_name__   , 0   , input_size - 1						)
						lowercase :							Optional[int]    		=time.time()
						return end - start






def 				_lowerCAmelCase			(   )				->  None:
						lowercase :							Optional[int]    		=[10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
						lowercase :							List[Any]    		=[time_max_subarray(__magic_name__						) for input_size in input_sizes]
						print('''No of Inputs\t\tTime Taken'''						)
						for input_size, runtime in zip(__magic_name__   , __magic_name__						):
												print(__magic_name__   , '''\t\t'''   , __magic_name__						)
						plt.plot(__magic_name__   , __magic_name__						)
						plt.xlabel('''Number of Inputs'''						)
						plt.ylabel('''Time taken in seconds'''						)
						plt.show()


if __name__ == "__main__":
							from doctest import testmod

							testmod()










import numpy as np







def  lowerCAmelCase_	(lowerCAmelCase__:		np.ndarray		,						lowerCAmelCase__:		float  ):





			"""simple docstring"""


			return np.where(vector > 0		,						lowerCAmelCase__		,						(alpha * (np.exp(lowerCAmelCase__  ) - 1))  )


if __name__ == "__main__":
	import doctest

	doctest.testmod()






